Is the friend of my friend my enemy?

Gabe Runte, Holly Moeller

University of California, Santa Barbara

Situating a model

On Mutualism

Theory predicts that cooperation is evolutionarily unstable in the absence of mechanisms that counteract the selective incentive to cheat
- M.E. Fredrickson

The mycorrhizal symbiosis

Partner preference

Theory predicts that cooperation is evolutionarily unstable in the absence of mechanisms that counteract the selective incentive to cheat
- M.E. Fredrickson

Partner preference

Partner preference exists
Additional information about the phenomenon

The mycorrhizal symbiosis

Partner preference

Quality assessment (ROI)

Theory predicts that cooperation is evolutionarily unstable in the absence of mechanisms that counteract the selective incentive to cheat
- M.E. Fredrickson

Return on Investment

Trees make decisions

Fungi make decisions

Somethin else

The mycorrhizal symbiosis

Partner preference

Quality assessment (ROI)

Theory predicts that cooperation is evolutionarily unstable in the absence of mechanisms that counteract the selective incentive to cheat
- M.E. Fredrickson

Building a model

A simple model

A (less) simple model

A mutualism network model

Next slide

Fungi connect to multiple trees (and vice versa)
Evidence for directed sharing of resources (Bogar 2022)
Fungi connect to multiple trees (and vice versa)
Evidence for directed sharing of resources (Bogar 2022)

Why modeling?

Define an explicit driver of experimental outcomes
Test our intuition for the way systems work
Identify key emperical knowledge gaps

Model schematic

DIAGRAM OF MODEL

Building the model

Assumptions:

Trees obtain vital resources from fungi (obligate)
All fungal resources come from host trees
The system has a fixed nitrogen budget

Building up to system complexity

One-Tree-One-Fungus

Axes of comparison

Why partner pref and ROI are interesting

Analyses

Implications

Many Thanks

Supplementary materials

Model formulation

\[\begin{eqnarray} \dot{B_i} &=& \rho_i N_i - (a_i+m_{B})B_i \\[2ex] \dot{C_i} &=& a_iB_i -C_i\sum_jr_{ij}\Psi_{ij} \\[2ex] \dot{F_j} &=& \sum_iC_ir_{ij}\Psi_{ij}-m_{F}F_j \\[2ex] \dot{N_i} &=& E \sum_ju_js_{ji}F_j\Upsilon_{ji}-m_{N}N_i \\[2ex] \dot{E} &=& -\sum_i\dot{N_i} \end{eqnarray}\]

Table of parameters

Class	Symbol	Units	Description
State variables	B	C	Biomass of host tree
	N	N	Host Nitrogen
	C	C	Host Carbon
	F	C	Fungal biomass
	E	N	Environmental N
Parameters	$\Psi$	None	Plant allocation based on N income
	$\Upsilon$	None	Fungal allocation based on carbon income
	$\rho$	C/Nt	Photosynthetic capacity
	a	1/t	allocation rate
	r	1/t	host preference for fungus
	s	1/t	Fungal preference for host
	u	1/Nt	fungal uptake rate
	e	C/C	fungal conversion efficiency